<!DOCTYPE html>
<html lang="en-US">
<!--********************************************-->
<!--*       Generated from PreTeXt source      *-->
<!--*                                          *-->
<!--*         https://pretextbook.org          *-->
<!--*                                          *-->
<!--********************************************-->
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<meta name="robots" content="noindex, nofollow">
</head>
<body class="ignore-math">
<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>Find the Fourier coefficients for <span class="process-math">\(f(x)\text{,}\)</span> with period <span class="process-math">\(2\pi\text{,}\)</span> given as</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
f(x)=2+4\sin x-0.5\cos 4x -99\sin 100x.
\end{equation*}
</div>
<p class="continuation">Since <span class="process-math">\(f(x)\)</span> here is already in terms of sine and cosine functions, there is no need to compute the Fourier coefficients. We just need to figure out where each term would fit, by comparing it with a Fourier series. Only the following Fourier coefficients are nonzero:</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
\frac{a_0}{2}=2,\quad b_1=4, \quad a_4=-0.5,\quad b_{100}=-99.
\end{equation*}
</div>
<span class="incontext"><a href="sec7_3.html#p-347" class="internal">in-context</a></span>
</body>
</html>
